Simplify Square Root of 69312

Here we will show you two methods that you can use to simplify the square root of 69312. In other words, we will show you how to find the square root of 69312 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√69312 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69312 to simplify the square root of 69312. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 69312. The factors of 69312 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 152, 192, 228, 304, 361, 456, 608, 722, 912, 1083, 1216, 1444, 1824, 2166, 2888, 3648, 4332, 5776, 8664, 11552, 17328, 23104, 34656, and 69312. Furthermore, the greatest perfect square on this list is 23104 and the square root of 23104 is 152. Therefore, A equals 152.

B = Calculate 69312 divided by the greatest perfect square from the list of all factors of 69312. We determined above that the greatest perfect square from the list of all factors of 69312 is 23104. Furthermore, 69312 divided by 23104 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 69312 in its simplest radical form as follows:

√69312 = A√B

√69312 = 152√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69312 to simplify the square root of 69312 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 69312 and then take the square root of that product. The prime factors that multiply together to make 69312 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 19 x 19. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 19 x 19 = 23104 and the square root of 23104 is 152. Therefore, A equals 152.

B = Divide 69312 by the number (A) squared. 152 squared is 23104 and 69312 divided by 23104 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 69312 in its simplest radical form as follows:

√69312 = A√B

√69312 = 152√3

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 69313
Here is the next square root on our list that we have simplifed for you.